A sequence is given by \(2\frac{1}{2}, 5, 7\frac{1}{2}, …..\) if the nth term is 25, find n
- 9
-
10
- 12
- 15
The correct answer is: B
Explanation
\(a = 2\frac{1}{2}, nth = a + (n-1)d \Rightarrow 25 = 2\frac{1}{2} + (n-1)2\frac{1}{2}\\25 = \frac{5}{2}+(n-1)\frac{5}{2} \Rightarrow 22\frac{1}{2} = \frac{5n-5}{2}\Rightarrow \frac{45}{2} = \frac{5n-5}{2}\\
45 = 5n - 5 \Rightarrow 5n = 50 \Rightarrow n = 10\)